Để pt có ng0 thì: \(\Delta'=\left(2m+5\right)^2-2m-1>0\)
\(\Leftrightarrow4m^2+2m+24>0\left(LĐ\right)\)
Theo Viet:\(x_1+x_2=4m+10;x_1x_2=2m+1\)
\(A^2=\left|x_1\right|+\left|x_2\right|-2\sqrt{x_1x_2}\)
\(A^2=\left|x_1\right|+\left|x_2\right|-2\sqrt{2m+1}\)
\(A^2=\sqrt{\left(x_1+x_2\right)^2}-2\sqrt{2m+1}\)
\(A^2=\sqrt{\left(4m+10\right)^2}-2\sqrt{2m+1}\)
Đến đây thì dễ rồi.
\(\left|\sqrt{x_1}\right|-\left|\sqrt{x_2}\right|\) ?